My dog chewed up the bill of my boyfriend's favorite hat. Is there anyway I can repair it, cheaply?

Question

I know the simpiliest solution would be to buy a new hat. However, not only does the current hat have sentimental value (although it's just a junky trucker hat), but it took me a good 20 minutes to find a picture of the hat online, and the site wasn't even in English! Very little of the hat is destroyed, only the front right of the bill, probably about a half of an inch in is missing. Is there any way I can repair the hat with a needle and thread and cheap materials from the arts and crafts store? My boyfriend and I are tight on cash and agreed on a strict 20 dollar budget for Christmas. I feel that repairing the hat and giving it back to him would be a great gift. My boyfriend is the type of guy who would definitely appreciate the effort, and I feel as if it's the thought that counts. I don't care if it doesn't look like new, I just want the missing chunk of the hat to not be noticeable, so my boyfriend can wear it again. The hat is very special to him. I'm not an expert on materials,

but the bill seems to be made out of some yellowish foam stuff and some black pasticy stuff. :) lol

Here's a picture of the hat:
http://www.buckleking.de/out/oxbaseshop/html/0/dyn_images/1/001787_breed_apart_zoom_p1.jpg

Oh, I'd also like to add that in the picture you can see several archs of stitching on the bill of the hat. The hat is only chewed to the outermost arch of stitching. Thanks so much!

Aw, I know how silly it is! But it is special to him, thank you for the answers so far! I'm looking into all my options!

Answer 1

Since it's just a narrow area, how about if you cut it even and then glue on a row of wide piping, available in the fabric store. You could buy white and then color it with a sharpie before you glue it on.
.

Answer 2

Try unstich the old bill,find another crap hat with the same bill and the **** on.How could A gay trucker hat have so much value??